Such a cutting unit is known, for example, from Netherlands Patent Application No. 7404738, (which corresponds substantially to U.S. Pat. No. 3,962,785). In this known construction the cutting members are forced on each other by means of a resilient element which is connected to the locking member. This pressure force is necessary to counteract those forces which occur instantaneously when a hair is cut and by which the cutting members would be urged apart. The pressure force of the resilient element of the known construction is present continuously and causes loss of energy and detrition of the moving parts.